Bayes Theorem in the Courtroom
Bayes Theorem in the Courtroom
Throughout the course of a criminal trial, there are many different pieces of evidence and alibis that jurors are to consider when determining the verdict. As would be expected there is usually conflicting pieces of evidence provided by the defense and prosecution and from this evidence the jury needs to determine the likelihood of either side’s story being true. In the article that is linked to, an assault trial was being discussed. In this trial much of the evidence pointed that the alleged perpetrator was innocent: a seemingly strong alibi, an appearance that didn’t match the accuser’s initial description, and the accuser was unable to identify him in a police lineup. On the other hand the alleged assailant was a DNA match based on a sample that the victim provided. The probability of a random person being a DNA match is 1 in 200 million. In this trial a statistician was called in by the defense as an expert witness to explain Bayes theorem to the jury. The aim was that the jury would avoid the prosecutor’s fallacy wherein the prosecution relies heavily on the result of a test like a DNA match, even though a false positive result may be more likely, even if the test is very accurate. This fallacy arises from a misunderstanding of conditional probability or Bayes rule. Ultimately the jury found the alleged assailant to be guilty.
The article also does a Bayesian analysis of the infamous OJ Simpson trial, which reached a conclusion that there was a 0.72 probability that OJ was guilty and a 0.99 probability that the LAPD framed Simpson. These probabilities conflict with the jury’s findings in the real case. This brings up the question, were the jury’s findings correct? Should the usage of Bayes theorem be commonplace in the courtroom.
As we learned in class, Bayes theorem is used to describe the probability of an event based on previous events or the knowledge of prior conditions. Oftentimes Bayes theorem can bring us to conclusions that differ from our initial assumptions based on the information. One of the examples used in class dealt with the idea of having a positive covid test with a 1% false positive rate, but occurring with an asymptomatic individual. Based on initial assumptions many would conclude that the likelihood of the individual having covid is 99%. However using Bayes theorem. When factoring in the prior probability of having Covid which was put at 2% the conditional probability of the individual having covid is 66%. This example helps to show how Bayes theorem can cause dissonance between one’s initial assumptions and the actual probabilities. As the linked article shows Bayes theorem can have implications in important real life scenarios like the courtroom and there is a conversation to be had about whether or not it should be used and how much it should be prioritized as evidence.
Link: https://www.ishinews.com/bayes-theorem-can-statistics-help-guide-a-verdict-in-the-courtroom/